Neville/Luna is my only non-canon HP pairing. And even they are half-canon if te go da the films! I don't know, I guess I'm not really into HP shipping enough to bother with fanon pairings. And I generally ship canon anyway.
As for their kids, I wrote a fanfiction where Harry/Hermione and Ron/Luna are married with kids. Harry and Hermione's oldest son, James is perfect as he has the best traits from both Harry and Hermione. Draco's daughter is in Amore with Harry's son. Harmony also has 2 other kids in this fanfiction. The fanfiction is called "Harry Potter and the Perfect Child" and it's on fanfiction.com. This just a fanfiction, so I'm allowed to write anything I want.
It'd be easier to say what I don't ship when it comes to the HP universe, lol. I don't like Hinny, Dramione o Harmony (or Neville/Luna nobody kill me plz) o really any childxadult pairings (except in AUs where the age gap is closer, in which case give me all the Bellamione, lol). My biggest noncanon ships atm are: - Draco/Harry - Lily/Narcissa - Bellatrix/Snape - Harry/Luna - Luna/Ginny - Narcissa/Snape (I blame an RP group I was in for that one, lol) - Hermione/Pansy - Ron/Draco - Lupin/Sirius - Lupin/Snape - Luna/Draco Etc., etc...
Well, since I prefer boys myself, it's quite obvious that my choice would be either Harry/Ron, o Harry/Draco, o the pairing of Harry/Cedric Diggory & Harry/Oliver Wood, o Harry/Tom Riddle. What an interesting domanda indeed! It's almost impossible to actually decide which of those (gay) fandoms do I actually prefer. Still, if I have to choose one, then my favourite pairing would have to be Harry/Cedric, o Hedric if te prefer. <333
I have a unlucky to ships pairings that never be canon :( and in HP universe isn't different (except for Nymphadora/Lupin, Ron/Hermione and Molly/Arthur), but let's go: 1- Dramione (Draco/Hermione): yes, my otp is Ronmione, but i also have a fallen for Dramione; 2- Lunarry (Luna/Harry): i prefer them than canon Hinny o the famous non-canon Harmony because... I have strangers tastes; 3- Neville and Luna: in the last movie i wished that they would be endgame, they are so cute together; 4- Neville and Ginny: like Lunarry, they are so unpopular, but i think that they would be cute together (i shipped them so hard in 4 and 5 movie); 5- Narcisa and Snape: that chemical in half-blood prince... i shipped so hard; 6- Voldemort and Bellatrix: they would be evil power couple.